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Exponentially small splitting of separatrices under fast quasiperiodic forcing
dc.contributor.author | Delshams Valdés, Amadeu |
dc.contributor.author | Gelfreich, Vassili |
dc.contributor.author | Jorba, Angel |
dc.contributor.author | Martínez-Seara Alonso, M. Teresa |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-05-08T17:21:16Z |
dc.date.available | 2007-05-08T17:21:16Z |
dc.date.created | 1997 |
dc.date.issued | 1997 |
dc.identifier.uri | http://hdl.handle.net/2117/949 |
dc.description.abstract | We consider fast quasiperiodic perturbations with two frequencies $(1/\varepsilon,\gamma/\varepsilon)$ of a pendulum, where $\gamma$ is the golden mean number. The complete system has a two-dimensional invariant torus in a neighbourhood of the saddle point. We study the splitting of the three-dimensional invariant manifolds associated to this torus. Provided that the perturbation amplitude is small enough with respect to $\varepsilon $, and some of its Fourier coefficients (the ones associated to Fibonacci numbers), are separated from zero, it is proved that the invariant manifolds split and that the value of the splitting, which turns out to be exponentially small with respect to $\varepsilon $, is correctly predicted by the Melnikov function. |
dc.format.extent | 42 |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Global analysis (Mathematics) |
dc.subject.lcsh | Hamiltonian dynamical systems |
dc.subject.lcsh | Lagrangian functions |
dc.subject.lcsh | Nonlinear Dynamics |
dc.subject.lcsh | Differential equations |
dc.subject.other | quasiperiodic forcing |
dc.title | Exponentially small splitting of separatrices under fast quasiperiodic forcing |
dc.type | Article |
dc.subject.lemac | Varietats (Matemàtica) |
dc.subject.lemac | Hamilton, Sistemes de |
dc.subject.lemac | Lagrange, Funcions de |
dc.subject.lemac | Partícules (Física nuclear) |
dc.subject.lemac | Equacions diferencials ordinàries |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34C Qualitative theory |
dc.subject.ams | Classificació AMS::58 Global analysis, analysis on manifolds |
dc.subject.ams | Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
dc.subject.ams | Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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